Search for the pair production of long-lived supersymmetric partners of the tau lepton in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the CMS experiment, this paper presents the first search for long-lived stau pair production employing a graph neural network to identify displaced tau leptons, resulting in improved exclusion limits on stau masses and decay lengths within gauge-mediated supersymmetry-breaking models.

The Gist

The Big Picture: Hunting for "Ghostly" Cousins

Imagine the universe is a giant, bustling party where particles are the guests. The Standard Model is the guest list we know and understand. Supersymmetry (SUSY) is a theory suggesting that for every guest at the party, there is a "twin" we haven't met yet. These twins are heavier and usually hide very well.

This paper is about hunting for a specific twin: the stau. The stau is the supersymmetric partner of the tau lepton (a heavy cousin of the electron).

In many theories, these twins appear and disappear instantly. But in this specific scenario, the stau is a bit different. It's like a guest who arrives at the party, wanders around the room for a noticeable amount of time, and then leaves. Because it lingers, it leaves a trail that looks different from the usual "instant" guests. The scientists at CERN's CMS experiment wanted to catch these "lingering" staus.

The Challenge: Finding a Needle in a Haystack

The problem is that the "haystack" (the background noise of the LHC collider) is massive. Every time protons smash together, they create thousands of particles. Most of these look like normal jets of debris.

The scientists were looking for a very specific signature:

1. Two "tau" particles appearing out of nowhere.
2. Missing energy: Because the stau decays into a tau and a nearly invisible "gravitino" (a ghost particle), some energy seems to vanish from the room.
3. The "Displaced" Clue: This is the most important part. Normal taus decay immediately at the collision point. These special stau-taus travel a few millimeters or centimeters away from the center before decaying. It's like seeing a firework that doesn't explode until it's already halfway across the sky.

The New Tool: A Smart "Displaced" Detector

The paper highlights a major upgrade in their search strategy. Previously, the tools used to identify tau particles were like security guards trained to spot people standing right at the front door. If someone wandered a few steps into the lobby before being identified, the guards often missed them or thought they were just regular noise.

To fix this, the team built a new, super-smart AI tool called DISTAU.

• The Analogy: Imagine the old tools were like a standard metal detector. The new DISTAU tool is like a detective with a 3D map and a magnifying glass. It looks at the "shape" of the particle trail and specifically knows how to spot a particle that started its journey a few steps away from the main entrance.
• This AI is based on a "Graph Neural Network," which is a type of math that looks at how particles are connected to each other, rather than just looking at them one by one.

The Search: 138 "Years" of Data

The team analyzed data collected between 2016 and 2018. They had a massive dataset equivalent to 138 inverse femtobarns (a unit of data volume). To put that in perspective, if you imagine the data as a library, they read through a library so huge that if you read one book a second, it would take you millions of years.

They set up a "trap" (the Signal Region) with very specific rules:

• Must have two tau particles that look "displaced" (wandering).
• Must have a lot of missing energy (the ghost particles).
• Must not have any other obvious "noise" (like extra electrons or muons).

The Results: The Party is Quiet

After running their sophisticated AI through all that data, the result was: No staus were found.

However, in science, finding nothing is still a huge discovery because it tells us where not to look.

• The Exclusion: They can now say with 95% confidence that if these stau twins exist, they cannot have certain weights (masses) or travel certain distances.
  • If they weigh between 126 and 260 GeV (in one scenario), they cannot be traveling a distance of 50 mm.
  • If they weigh 200 GeV, they cannot be traveling between 21 and 94 mm.
• The Improvement: Their new AI tool (DISTAU) made the search much better than previous attempts. They could rule out more possibilities than ever before, effectively shrinking the "safe zone" where these particles could be hiding.

Why This Matters

Even though they didn't find the stau, they pushed the boundaries of our knowledge.

• Before: We knew staus couldn't be too light or too heavy in certain scenarios.
• Now: We know they definitely aren't in this specific "middle ground" of weight and travel distance.

It's like searching for a lost key in a house. You check the kitchen, the living room, and the bedroom. You don't find it, but now you know for sure it's not in those rooms. You have to look in the basement or the attic next time. This paper effectively cleared out a large section of the "basement" of the universe's parameter space, forcing future theories to be more precise about where these elusive particles might be hiding.

In short: The scientists used a brand-new, AI-powered "displaced particle detector" to scan a massive amount of collision data. They didn't find the ghostly stau twins, but they successfully proved that if the twins are there, they aren't hiding in the specific spot they were looking at. This makes the search for Supersymmetry more focused and efficient.

Technical Summary

Technical Summary: Search for Pair Production of Long-Lived Staus in Proton-Proton Collisions at $\sqrt{s} = 13$ TeV

Problem and Motivation
Gauge-mediated supersymmetry-breaking (GMSB) models provide a compelling framework for physics beyond the Standard Model (SM), particularly in addressing the hierarchy problem and offering a dark matter candidate (the gravitino). In these scenarios, the stau ($\tilde{\tau}$), the supersymmetric partner of the tau lepton, is often the next-to-lightest supersymmetric particle (NLSP). Due to the suppressed coupling between the stau, the tau, and the nearly massless gravitino ($\tilde{G}$), the stau can possess a macroscopic lifetime, decaying within the detector volume. This results in "displaced" decay vertices, where the resulting tau leptons originate significantly away from the primary proton-proton interaction point.

Existing searches for long-lived staus have faced limitations. Traditional hadronic tau ($\tau_h$) identification algorithms, optimized for prompt decays, suffer a rapid loss in efficiency (dropping by $\approx 95\%$ at transverse displacements of $\sim 10$ mm) as the decay vertex moves further from the beam axis. This paper addresses the need for a dedicated search strategy capable of identifying staus with proper decay lengths ($c\tau_0$) ranging from 1 to 1000 mm, specifically targeting the decay mode where both staus decay hadronically ($\tilde{\tau} \to \tau \tilde{G}$).

Methodology
The analysis utilizes proton-proton collision data collected by the CMS experiment at the LHC between 2016 and 2018, corresponding to an integrated luminosity of $138 \text{ fb}^{-1}$ at $\sqrt{s} = 13$ TeV.

• Signal Model: The search assumes simplified GMSB models where stau pairs are produced and decay into a tau lepton and a gravitino. Two scenarios are considered: a "maximally mixed" scenario (production of the lighter mass eigenstate $\tilde{\tau}_1$) and a "mass-degenerate" scenario (production of both $\tilde{\tau}_L$ and $\tilde{\tau}_R$).
• Event Reconstruction and Selection: Events are selected requiring large missing transverse momentum ($p_T^{\text{miss}} > 120$ GeV) and exactly two hadronic tau candidates. To reject SM backgrounds, events containing veto-electrons, veto-muons, or b-tagged jets are discarded.
• The DISTAU Algorithm: The core innovation of this work is the application of the DISTAU identification algorithm. This is a graph neural network based on the PARTICLENET architecture, specifically trained to distinguish displaced hadronic tau candidates ($\tau_h^{\text{dis}}$) from background jets. Unlike standard algorithms, DISTAU utilizes features relevant to displaced decays, such as the impact parameters of charged constituent tracks, while maintaining sensitivity to hadronic tau properties. The algorithm operates with three working points (loose, medium, tight), with the "tight" point ($WPT$) requiring a transverse impact parameter $|d_{xy}| > 2$ mm and a significance $\hat{d}_{xy} > 5$.
• Background Estimation: The dominant background arises from SM jets misidentified as displaced taus. Since simulation is insufficient for modeling the tails of the kinematic distributions, a data-driven method is employed. Misidentification probabilities are measured in control regions enriched in $W$+jets and Drell-Yan ($Z/\gamma^* \to \tau\tau$)+jets events. These probabilities are parametrized as a function of jet $p_T$ and $|d_{xy}|$ and extrapolated to the signal region (SR).
• Statistical Analysis: The signal region is divided into eight bins based on the subleading tau $p_T$, $p_T^{\text{miss}}$, and the stransverse mass ($m_{T2}$). A profile likelihood ratio test statistic is used to set upper limits on the production cross-section at 95% confidence level (CL), incorporating systematic uncertainties from theory, detector performance, and background estimation.

Key Contributions

1. First Application of DISTAU: This paper presents the first search for long-lived staus utilizing the DISTAU graph neural network algorithm, which is specifically designed to recover efficiency for tau leptons decaying far from the primary vertex.
2. Extended Parameter Space: The analysis covers a broad range of stau masses ($m_{\tilde{\tau}}$) from 90 to 600 GeV and proper decay lengths ($c\tau_0$) from 1 to 1000 mm, filling gaps left by previous searches that were limited to prompt decays or very long lifetimes.
3. Improved Background Modeling: By employing a robust data-driven technique using control regions and cross-checks between $W$+jets and Drell-Yan samples, the analysis minimizes reliance on simulation for the dominant misidentified-jet background.

Results
The analysis observed no significant excess of events over the predicted SM background. The observed event yields in all eight signal bins were consistent with the background-only hypothesis. Consequently, exclusion limits were set on the stau pair production cross-section.

• Exclusion Limits (Maximally Mixed Scenario): Stau masses in the range 126–260 GeV are excluded for a proper decay length of $c\tau_0 = 50$ mm. For a stau mass of $m_{\tilde{\tau}} = 200$ GeV, proper decay lengths in the range 21–94 mm are excluded.
• Exclusion Limits (Mass-Degenerate Scenario): Due to a higher production cross-section, the limits are stronger. Stau masses in the range 90–425 GeV are excluded for $c\tau_0 = 50$ mm. For $m_{\tilde{\tau}} = 200$ GeV, the excluded decay length range is 6–333 mm.
• Performance: The results improve upon previous exclusion limits reported by ATLAS and CMS. For example, at $m_{\tilde{\tau}} = 300$ GeV in the mass-degenerate scenario, the upper limits on the cross-section are improved by a factor of 2.5 to 5.7 compared to previous searches, depending on the decay length.

Significance
The paper claims that the development and application of the dedicated DISTAU algorithm have led to a significant improvement in experimental sensitivity to long-lived stau signatures. By successfully identifying displaced tau leptons that would have been missed by standard reconstruction methods, this search extends the explored parameter space for supersymmetry. The results provide the most stringent constraints to date on GMSB scenarios involving long-lived staus decaying within the CMS tracker volume, effectively ruling out specific regions of the $m_{\tilde{\tau}}$ vs. $c\tau_0$ parameter space. The analysis demonstrates the viability of using graph neural networks to tackle non-standard signatures in high-energy physics, offering a template for future searches for displaced objects.